Question

An air bubble of radius $1 \, mm$ is located at a depth of $20 \, cm$ below water level. The excess pressure inside the bubble above the atmospheric pressure is [Given, the surface tension of water is $0.075 \, Nm^{- 1}$ and density is $1000 \, kg \, m^{- 3}$ ]

• A. $2110Pa$
• B. $2210Pa$
• C. $2260Pa$
• D. $2310Pa$

Answer 1

Answer: (A)

Let the atmospheric pressure be $P_{0}$
Pressure just outside the bubble,
$P=P_{0}+hρg$
Pressure of air inside the bubble
$P_{in}=R+\frac{2 \sigma }{r};\sigma $ is surface tension
$P_{in}=P_{0}+hρg+\frac{2 \sigma }{r}$
$\therefore P^{'}-P_{0}=\frac{1}{5}\times 1000\times 9.8+\frac{2 \times 0 . 075}{1 \times 10^{- 3}}$
$=1960+150$
$=2110Pa$